Scott Morrison is open to the Christchurch mosque terrorist in Australia.
Home Affairs Minister Peter Dutton is seeking legal advice on the potential trans-Tasman transfer.
for Brenton Tarrant to be sent back to Australia after being convicted of killing 51 people and wounding 40 others.
Mr Morrison discussed the Australian gunman's case with Jacinda Ardern after his sentencing in New Zealand.
"I know all Australians and New Zealanders want to see this character locked up to never see the light of day again - I agree with that," the prime minister said on Friday.
"Whether he is held in New Zealand or Australia, we're open to that discussion."
The gunman, a violent right-wing extremist and white supremacist, will spend the rest of his life behind bars for the March 2019 mass murders.
There would need to be some changes to legal arrangements between Australia and New Zealand for the transfer to happen.
New Zealand is not a signatory to the relevant legislation involved and Mr Peters has no appetite to sign up.
The prime minister said he and Ms Ardern would work through the issues involved.
"Mostly, we're concerned about what the views of the families would be, of those affected, and we want to do the right thing by them," Mr Morrison said.
"There has been no request made for that (transfer), I should stress."
Mr Dutton has asked for legal advice and pledged to work closely with New Zealand.
"We'd have to look at what happens in terms of parole or the way in which our legal system would work here," he said.
"So, the first priority is to keep him in jail for the rest of his life, and we'll work very closely with New Zealand on any requests that they provide."
